A037121 Trajectory of 3 under map n -> 47n+1 if n odd, n->n/2 if n even.
3, 142, 71, 3338, 1669, 78444, 39222, 19611, 921718, 460859, 21660374, 10830187, 509018790, 254509395, 11961941566, 5980970783, 281105626802, 140552813401, 6605982229848, 3302991114924, 1651495557462
Offset: 0
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Mathematica
NestList[If[EvenQ[#],#/2,47#+1]&,3,30] (* Harvey P. Dale, May 05 2014 *)